The present invention relates to a resolution conversion method for converting a resolution of a binary image represented in the dot-matrix format.
In the technical field of the resolution conversion of an image, the liner interpolating method (for instance, set forth in Tokkaihei 5-219360, Japanese Non-Examined Patent Publication) and the area averaging method (for instance, set forth in Tokkaihei 5-40825 and Tokkai 2006-270707, both Japanese Non-Examined Patent Publication) are generally employed for this purpose. With respect to the binary image, after the resolution conversion processing is completed, the binarizing processing is further applied to each of the pixels included in the image concerned, by comparing densities and threshold values of the pixels with each other.
FIG. 14 shows a schematic diagram indicating appropriate application ranges of the liner interpolating method, the area averaging method, etc. Generally speaking, although an interpolating method, such as the liner interpolating method, etc., is employed for acquiring a high resolution image (size enlargement) and a slightly low resolution image (size reduction), there has been a problem that jaggies are liable to emerge in the reproduced image when the interpolating method is employed for performing an excessively low resolution processing to such an extent that the image size is heavily reduced on a scale of one to several. To avoid such the problem, the area averaging method has been usually employed only for acquiring a low resolution image (size reduction). On the other hand, although the area averaging method is beneficial for acquiring a low resolution image, an effect of the edge smoothing operation in which the high resolution property is effectively utilized becomes insufficient when the area averaging method is employed for acquiring the high resolution image.
Accordingly, there has been considered such a method including the steps of: converting the original binary image to the multi-value image by applying an interpolating processing, such as the liner interpolation processing, etc.; and applying the area averaging to the multi-value image ((interpolation+area averaging) method). According to the abovementioned method, since the problems residing in both the interpolating method and the area averaging method can be complemented with each other, it is possible to acquire a resolution converted image, serving as a high quality image to some extent, without depending on the magnification factor over the high to low resolution conversion processing.
FIG. 15 shows a flowchart indicating a resolution conversion processing flow of a binary image according to the (interpolation+area averaging) method. Initially, the binary image represented in the dot-matrix format is converted to the multi value image by repeatedly finding a density value (interpolation value) at an arbitral position between two pixels of the binary image for every pixel included in the binary image (Step S301). Successively, a density value of each pixel to be included in the output image is found by performing the operation for re-sampling the multi-value image, while employing the area averaging method (Step S302). Then, each of output pixels is binarized by comparing the density value, found in the above, with a predetermined threshold value so as to determine 0 or 1 corresponding to small or large (Step S303).
For instance, as shown in FIG. 16, an input image 311 and an output image 312 are correlated with each other by superimposing them with each other so as to make the pixels positioned at the four corners of the input image 311 and the other pixels positioned at the four corners of the output image 312 coincide with each other, and then, the total area of the output image 312 is equally divided by the number of output pixels, so as to allot an image area G to each of the pixels of the output image 312. In this connection, hereinafter, the center position of the image area G is defined as a coordinate position representing the image area G concerned (area represented coordinate; pixel position).
In the abovementioned example, the following assumptions are fulfilled:
1) setting a pixel area (specified by a coordinate area in both a horizontal direction and a vertical direction) so as to make it correspond to a rectangular area occupied by each of pixels;
2) setting a coordinate area No. k at a coordinate value in a range of (k−0.5)-(k+0.5);
3) setting a represented coordinate of the coordinate area No. k at value k serving as the center value of the coordinate area;
4) setting the image area as the rectangular area having apexes, each of which is a center of each of four pixels residing at four corners of the image area concerned; and
5) applying the assumptions for the output image to those of the input image as well.
Further, as shown in FIG. 17, the pixels of the input image 311 correspond to those of the output image 312, so that the centers of four pixels positioned at four corners of the input image 311 coincide with those of the output image 312.
When multiplying the resolution with the non-integer magnification factor, a phase relationship between each of the pixels of the input image and each of the pixels of the output image varies depending on its current position. For instance, when multiplying the resolution with the magnification factor of 205%, which is slightly shifted from a double size of the input image, the change between the phase relationship shown in FIG. 18 and the other phase relationship shown in FIG. 19 alternately emerges with a long time period. In this connection, in both FIG. 18 and FIG. 19, white circles indicate white pixels, black solid circles indicate black pixels, small-sized gray solid circles indicate output pixels, and a rectangular area, written in broken lines and surrounding each of the output pixels, indicates each of pixel areas (integration region) in regard to a corresponding one of the output pixels.
At each of the positions having the phase relationship shown in FIG. 18, a plurality of pixels (peripheral four output pixels), which are uniformly influenced by a value of a specific pixel included in the input image, are generated around the peripheral area of the specific pixel. Concretely speaking, the four output pixels (indicated by the small-sized gray solid circles) residing around the peripheral area of a black input pixel B are made to be black by strongly receiving the influence of the black input pixel B positioned at the center of the four output pixels, while the other four output pixels residing around the peripheral area of a white input pixel W are made to be white by strongly receiving the influence of the white input pixel W positioned at the center of the four output pixels concerned. Accordingly, since a single input pixel is merely replaced by four output pixels, it is impossible to smooth the edge of the diagonal, as shown in FIG. 20, resulting in a difficulty of acquiring the effect of the high resolution processing.
On the other hand, at each of the positions having the phase relationship shown in FIG. 19, the pixel area, to which hatched lines are not applied, is strongly influenced by a specific input pixel (input pixel positioned at a center of the pixel area of the output pixel concerned). Accordingly, if the specific input pixel is white, the concerned pixel area is securely made to be white, while if the specific input pixel is black, the concerned pixel area is securely made to be black, resulting in the stable binarizing processing. On the other hand, the other pixel area, to which hatched lines are applied, is uniformly influenced by the peripheral input pixels without depending on the specific input pixel (for instance, an image area 331 is uniformly influenced by both a black input pixel 332 and a white input pixel 333, when viewing them in the vertical direction). Accordingly, the density value derived by normalizing the integration value is liable to approach the threshold value, and as a result, when performing the binarizing processing, the operation for determining whether the concerned pixel area is made to be white or black is liable to become unstable. Therefore, according to such the phase relationship shown in FIG. 19, there would occur such the phenomenon that the line thickness of the diagonal discontinuously becomes thick or thin as shown in FIG. 21.
Further, depending on the phase relationship between the input pixel and the output pixel, the edge of the diagonal is appropriately smoothed.
As mentioned in the foregoing, since the phase relationship between the input pixel and the output pixel gradually varies within a single sheet of image when the high resolution multiplying operation with a non-integer magnification factor is applied, there has been such a problem that unevenness is generated in the smoothing state of the edge of the diagonal.
Further, when the high resolution multiplying operation with an integer magnification factor is applied, there has been another problem that the tendency shown in any one of FIG. 18 or FIG. 19 emerges all over the image.